A048113 - OEIS

A048113

Triangular array T read by rows: T(h,k) = number of paths consisting of steps from (1,1) to (h,k) such that each step has length 1 directed up or right and each vertex (i,j) satisfies i/2<=j<=2i, for h=0,1,2,... and k=0,1,2,...

%I #17 Oct 19 2020 03:43:16

%S 0,0,0,0,1,0,0,1,1,0,0,0,2,0,0,0,0,2,2,0,0,0,0,2,4,2,0,0,0,0,0,6,6,0,

%T 0,0,0,0,0,6,12,6,0,0,0,0,0,0,6,18,18,6,0,0,0,0,0,0,0,24,36,24,0,0,0,

%U 0,0,0,0,0,24,60,60,24,0,0,0,0,0,0,0,0,24,84,120,84,24,0,0,0,0

%N Triangular array T read by rows: T(h,k) = number of paths consisting of steps from (1,1) to (h,k) such that each step has length 1 directed up or right and each vertex (i,j) satisfies i/2<=j<=2i, for h=0,1,2,... and k=0,1,2,...

%H Alois P. Heinz, <a href="/A048113/b048113.txt">Rows n = 0..200, flattened</a>

%e Rows: {0}; {0,0}; {0,1,0}; {0,1,1,0}; ...

%t T[0, 0] = T[0, 1] = T[1, 0] = 0; T[1, 1] = T[2, 1] = T[1, 2] = 1; T[h_, k_] /; Not[h/2 <= k <= 2h] = 0; T[h_, k_] := T[h, k] = If[h-1 >= k/2, T[h-1, k], 0] + If[k-1 >= h/2, T[h, k-1], 0]; row[s_] := Table[T[h, s-h], {h, 0, s}]; Table[row[s], {s, 0, 12}] // Flatten (* _Jean-François Alcover_, Dec 02 2016 *)

%Y Cf. A048116.

%K nonn,tabl,walk

%O 0,13

%A _Clark Kimberling_

%E Offset changed to 0 by _Alois P. Heinz_, Oct 06 2016